Elsevier

Magnetic Resonance Imaging

Volume 26, Issue 7, September 2008, Pages 1015-1025
Magnetic Resonance Imaging

Review Articles
On the use of information theory for the analysis of the relationship between neural and imaging signals

https://doi.org/10.1016/j.mri.2008.02.019Get rights and content

Abstract

Functional magnetic resonance imaging (fMRI) is a widely used method for studying the neural basis of cognition and of sensory function. A potential problem in the interpretation of fMRI data is that fMRI measures neural activity only indirectly, as a local change of deoxyhemoglobin concentration due to the metabolic demands of neural function. To build correct sensory and cognitive maps in the human brain, it is thus crucial to understand whether fMRI and neural activity convey the same type of information about external correlates. While a substantial experimental effort has been devoted to the simultaneous recordings of hemodynamic and neural signals, so far, the development of analysis methods that elucidate how neural and hemodynamic signals represent sensory information has received less attention. In this article, we critically review why the analytical framework of information theory, the mathematical theory of communication, is ideally suited to this purpose. We review the principles of information theory and explain how they could be applied to the analysis of fMRI and neural signals. We show that a critical advantage of information theory over more traditional analysis paradigms commonly used in the fMRI literature is that it can elucidate, within a single framework, whether an empirically observed correlation between neural and fMRI signals reflects either a similar stimulus tuning or a common source of variability unrelated to the external stimuli. In addition, information theory determines the extent to which these shared sources of stimulus signal and of variability lead fMRI and neural signals to convey similar information about external correlates. We then illustrate the formalism by applying it to the analysis of the information carried by different bands of the local field potential. We conclude by discussing the current methodological challenges that need to be addressed to make the information-theoretic approach more robustly applicable to the simultaneous recordings of neural and imaging data.

Introduction

Functional magnetic resonance imaging (fMRI) [1], [2] is the most widely used tool to investigate sensory and cognitive processes in the human brain. A potential problem in the interpretation of fMRI data is that the blood-oxygenation-level-dependent (BOLD) signal obtained with fMRI measures neural activity only indirectly, as a local change of deoxyhemoglobin concentration due to the metabolic demands of neural function. To build and interpret correctly sensory and cognitive maps in the human brain, it is thus crucial to understand what the BOLD signal means in terms of neural activation. The necessity to address this question has led in recent years to a substantial experimental effort for the simultaneous recordings of hemodynamic and neural signals [3], [4], [5], [6], [7], [8]. These studies revealed that the BOLD signal, far from reflecting simply the discharge rate of the neural populations in a voxel, is instead a complex and rich function of the dynamic state of the network (including the balance of excitation and inhibition, synaptic activity and neuromodulation) and correlates partially with a number of massed neural signals reflecting the functional network configuration. In particular, BOLD signal changes correlate with variations (over a wide frequency range) of local field potential (LFP) fluctuations [4], [5], [8], [9]. LFPs reflect the fluctuations in the input and the intracortical processing of the local cortical network, including the overall effect of population synaptic potentials [10], [11] and other types of slow activity such as spike afterpotentials and voltage-dependent membrane oscillations [12], [13], [14], [15]. The BOLD signal also correlates (though less robustly) to multiunit activity, which mostly reflects the massed spike discharge rate of larger neurons around the electrode [4], [16].

The complexity of the relationships between BOLD and neural signals makes it difficult to interpret the sensory and cognitive maps obtained with fMRI in terms of the cortical computation and the information encoding performed by the neuronal network during stimulation. A thorough and quantitative investigation of the information about sensory and cognitive tasks conveyed by the different types of extracellular field potentials, such as LFP, MUA and single unit activity, and the information conveyed by the associated BOLD signal is therefore essential for our understanding of the neurovascular coupling and of the meaning of fMRI maps.

Despite the experimental progress in the simultaneous recordings of fMRI and neural signals, so far, relatively little attention has been devoted to the development of analysis methods that can best elucidate how neural and hemodynamic signals represent sensory information. In this article, we propose that the analytical framework of information theory [17], the mathematical theory of communication, is ideally suited to this purpose. We review the principles of information-theoretic analysis of multiple signals. While this theory has been developed in previous studies, it has been used and discussed so far mainly in the spike train analysis literature. Here, we thus focus on how this could be applied to the analysis of fMRI and neural signals. We show that a critical advantage of information theory over more traditional analysis paradigms commonly used in the fMRI literature is that it can elucidate, within a single framework, which signals convey the most information about external stimuli or cognitive tasks, what features of each signal are most informative, which signals are most correlated to each other and which signals convey either the same or different information about the stimuli. In addition, information theory can determine whether an empirically observed correlation between neural and fMRI signals reflects either a similar stimulus tuning or a common source of variability unrelated to the external stimuli (such as neuromodulation). It also determines the extent to which these shared sources of stimulus signal and of variability lead fMRI and neural signals to convey similar information about external correlates. We then illustrate the formalism by applying it to the analysis of the information carried by different bands of the LFPs recorded in the primary visual cortex. The reason for presenting this analysis is that understanding the information content of LFPs is important toward understanding what type of neural representation of events may be reflected into the BOLD signal. Furthermore, a conceptually similar analysis may be applied to fMRI data. Finally, we discuss the most urgent methodological challenges that need to be addressed to make the information-theoretic approach more robustly applicable to simultaneous recordings of neural and imaging data.

Section snippets

Information theory

The aim of information-theoretic analysis is to get insight into how neurons or, more generally, physiological signals reflecting neural activity encode and represent information. For example, we might want to know whether a particular neuron conveys information by the total number of emitted spikes (the “spike count”) or by temporal patterns of spikes, or we may want to know which LFP band conveys the most information about the stimulus. In carrying out such an analysis, the first step is to

Information carried by the joint observation of different brain signals and their redundancy

The above single-signal information analysis can be extended to compute how much information about the stimulus can be obtained when combining together two signals X and Y. Since information can be applied to any type of signal, X and Y may be two signals of a very different nature, for example, X from spikes and Y from the concurrently recorded BOLD signal. Alternatively, X and Y may be a different quantification of the same neural signal (e.g., two different bands of the LFP recorded from an

Decomposition of redundancy in terms of correlations at fixed sensory input and correlations at different sensory inputs

When redundancy is zero, the joint information behaves as if the two signals had a completely independent stimulus tuning. Thus, the case of zero redundancy is defined as “information independence.” If signals X and Y originate from completely unrelated neural processes and, thus, does not share either a common source of modulation by the stimulus or any other type of covariation, their redundancy would be zero. Unlike the interpretation of positive redundancy, however, which necessarily

Examples of application to slow and fast LFP fluctuations in response to natural movies

To illustrate the application of this formalism to the joint analysis of different types of signal, we consider a sample analysis of LFPs recorded from the primary visual cortex of an anesthetized macaque in response to a binocularly presented naturalistic color movie. Full details on the experimental procedures are reported in Refs. [33], [34], [35]. Each recording site (seven in total from this animal) corresponded to a well-defined V1 visual receptive field within the field of movie

Statistical problems to be addressed for the application of information theory to fMRI

The most important practical problem in the successful application of the described formalism to neural and, in particular, imaging data is that calculation of information requires accurate estimation of the stimulus–response probabilities. Unfortunately, these probabilities are not known but have to be measured experimentally from the limited number of trials in which the neurophysiological or imaging data were recorded. The estimated probabilities are subject to statistical error and

Conclusions

The relationships between different neural and hemodynamic signals are complex. As a result, we need a nonlinear analysis framework to characterize all the possible implications of these complex relationships. We believe that once the above technical problems are studied and addressed, the information-theoretic formalism critically reviewed here will become an important tool for the investigation of sensory maps based on fMRI and for the analysis and interpretation of joint recordings of

Acknowledgments

This work was supported by IIT, by the Max Planck Society and by EPSRC EP/C010841, EP/E002331 and EP/E057101. We are indebted to M.A. Montemurro for developing with us most of the information-theoretic Matlab code used here and to A. Belitski, M.A. Montemurro, Y. Murayama, M.J. Rasch, G. Pola, F. Montani, C. Porro, P. Baraldi, D. Borla, N. Brunel, A. Mazzoni and A. Gretton for valuable collaboration and useful discussions on some of the topics covered in this article.

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